Question

Suppose that a two-year bond with a principal of $100 provides coupons at the rate of 6% per annum semiannually. Suppose that the zero-rates are

Maturity (years)	Zero Rate (%)
0.5	5.0
1.0	5.8
1.5	6.4
2.0	6.8

What is the bond's yield to maturity expressed with the continuous compounding?

- please use the formulas and explain step by step

Answer 1

As the bond is a semiannual bond, Coupon=Par*Coupon rate/2=100*6%/2=3

Present value of cash flows=CF*e^(-r*t)

The bond will give 3 for 2 years and additional 100 at the end of 2 years

Price of the bond=Sum of Present value of cash flows=3*e^(-5%*0.5)+3*e^(-5.8%*1)+3*e^(-6.4%*1.5)+3*e^(-6.8%*2)+100*e^(-6.8%*2)=98.38506

Using financial calculator
N=2*2
PMT=3
PV=-98.38506
FV=100
CPT I/Y=3.4390%

Hence, yield expressed in continuous compounding=ln((1+semiannual rate)^2)=ln((1+3.4390%)^2)=6.7624%